Triangular Number

  Triangular Number 

The triangular number sequence is the representation of the numbers in the form of equilateral triangle arranged in a series or sequence.

This is the Triangular Number Sequence:

1, 3, 6, 10, 15, 21, 28, 36, 45, ...

It is simply the number of dots in each triangular pattern:

We can use x_n to mean "dots in triangle n", so we get the rule:

Rule: x_n = n(n+1)/2

Example: the 5th Triangular Number is

x₅ = 5(5+1)/2 = 15

Example: the 60th is

x₆₀ = 60(60+1)/2 = 1830